the angular acceleration of flywheel having moment of inertia 50 kg `m^2` when a torque of 5 `N-m` is applied on the flywheel is

Options

A. `0.1 rad s^-2`
B. `250 rad s^-2`
C. `10 rad s^-2`
D. `1.25 rad s^-2 `

Answer

To find the angular acceleration of the flywheel, we can use the relationship between torque (τ), moment of inertia (I), and angular acceleration (α), which is given by the formula:

\[ \tau = I \cdot \alpha \]

Where:
- τ (tau) is the torque applied,
- I is the moment of inertia,
- α (alpha) is the angular acceleration.

### Step-by-Step Solution:

1. **Identify the given values**:
- Moment of inertia, \( I = 50 \, \text{kg} \cdot \text{m}^2 \)
- Torque, \( \tau = 5 \, \text{N} \cdot \text{m} \)

2. **Rearrange the formula to solve for angular acceleration (α)**:
\[ \alpha = \frac{\tau}{I} \]

3. **Substitute the known values into the equation**:
\[ \alpha = \frac{5 \, \text{N} \cdot \text{m}}{50 \, \text{kg} \cdot \text{m}^2} \]

4. **Calculate the angular acceleration**:
\[ \alpha = \frac{5}{50} = \frac{1}{10} = 0.1 \, \text{rad/s}^2 \]

5. **Conclusion**:
The angular acceleration of the flywheel is \( 0.1 \, \text{rad/s}^2 \).